Don Mango
Director of R&D, GE Insurance Solutions
CAS Vice President, Research and
Development

GE Insurance Solutions protects people, property and reputations. With over $50bn in combined assets, the GE Insurance Solutions group of companies is one of the world’s leading providers of commercial insurance, reinsurance and risk management services.
Life, Health, Property and Casualty
PROPRIETARY INFORMATION NOTICE
The information contained in this document is the property of Employers
Reinsurance Corporation, a member of the GE Insurance Solutions group of companies. It should not be reprinted, redistributed or disclosed to others without the express written consent of ERC.
© 2005 Employers Reinsurance Corporation
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© 2005 Employers Reinsurance Corporation
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Context: Asking Price model reflecting frictional capital costs
Insurance capital is a Shared Asset
Two distinct types of usage: consumptive and non-consumptive
More appropriate financial analogue than IRR:
Letter-of-Grant (~letter of credit)
Advocates EVA as decision metric
© 2005 Employers Reinsurance Corporation
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Broker Market, Large Treaty Placements
(I) Seeking Quotes (II) Market Price Formation (III) Filling Slip
RE #1
RE #2
RE #3
•Loss Cost estimate
•Expenses
•Targeted Profit Margin
•Strategy Differential
•Sum = ASKING Price
Initial Asking
Prices
BROKER
•
•Must factor in Cedant’s BID
Price
•Consider the range of asking prices
Soft factors
RE #1
RE #2
RE #n
•Any reinsurer on the
Approved List
•Given “the Price”
•Decision becomes a
Question of Volume
•Need Price Evaluation
LEADING MARKETS
ONLY
ANYONE WITH A
PULSE
© 2005 Employers Reinsurance Corporation
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Initial Asking
Prices
•Loss Cost estimate
•Expenses
•Targeted Profit Margin
•Strategy Differential
•Sum = ASKING Price
Quotes Will
Vary Due To
• Proprietary Loss Cost models
• Internal expense loads
• Strategy Differential (aggressive or averse signaling)
• Profit Margin – e.g.
> Based on marginal impact to portfolio own
> Based on own funky cost of capital model
> Based on ownership’s economic rent profit targets
If Ask X is much higher than others:
> May steer final price upward
> May indicate lack of interest
> May result in lower share being proposed
If Ask X is much lower than others:
> May steer final price downward
> May indicate strong interest
> May result in higher share being proposed
Conclusions:
> Signaling power in Quote
> Limited arbitrage opportunity
© 2005 Employers Reinsurance Corporation
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1) Liquidity requires diversity of opinion and losers
2) Anti-trust
3) Parameter uncertainty
4) Information asymmetry
5) …
Room For Different Asking Price Approaches
© 2005 Employers Reinsurance Corporation
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© 2005 Employers Reinsurance Corporation
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Merton-Perold: “risk capital” for a business unit should be cost of parental guarantee to make up any operating shortfall
Valuing this guarantee is easy when there are capital market equivalents
What about low liquidity, informationally opaque guarantees?
> E.g., Insurer portfolio of liabilities
Insurer provides shortfall guarantee to each policy it underwrites
Guarantee is issued by the entity in total, similar to a Letter of Credit
(LOC)
Exercise of guarantee by product segment depends on:
> Volatility
> Price adequacy
> Reserve adequacy
Company must manage the timing and size of guarantee exercises
(i.e., an internal bank run)
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• Legitimate standing as a counterparty is essential to their market viability  claimspaying rating
• Key rating variable is capital adequacy ratio (CAR) = Actual
Capital / Required Capital
• Each rating has a minimum
CAR associated with it
• If Actual Capital is fixed, then there is a maximum Required
Capital constraint
• Required Capital = fn(Premium, Reserves,
Assets)
• For planning purposes, assume reserves and assets are fixed  Required Capital constraint really means a
Premium Constraint
• Required Premium Capital = excellent proxy for underwriting capacity
© 2005 Employers Reinsurance Corporation
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• Underwriting activity generates required capital
> Either Current Year
Premium or Reserves
• Since insurer is subject to a maximum Required
Capital, underwriting activity occupies available capacity
• Longer duration business occupies capacity for a longer time
• Any occupation of capacity precludes the insurer from using that capacity to underwrite other products
• Clear opportunity cost
© 2005 Employers Reinsurance Corporation
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Required Premium Capital As Capacity Constraint
Balance
PLAN
Required
Capital Required
Factor Capital
Premium 600
Reserves 1,000
50%
40%
300
400
Assets 3,000
Actual Capital 2,000
Actual CAR 200%
Min CAR 200%
10% 300
1,000
IMPACT OF
RESERVE STRENGTHENING
Required
Capital Required
Balance Factor Capital
50% 210 420
1,100 40% 440
3,000
1,900
200%
200%
10% 300
950
© 2005 Employers Reinsurance Corporation
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Asset Owners:
• Control Overall Access Rights
•Preserve Against Depletion From Over-Use
User 1
Shared Asset
Reservoir, Golf Course,
Pasture, Hotel, …
Insurer Capital
• Consumes On
Standalone Basis
• Tunnel Vision - No
Awareness Of The Whole User 2
User 3
© 2005 Employers Reinsurance Corporation
User 4
• Consumes On
Standalone Basis
• Tunnel Vision - No
Awareness Of The Whole
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Consumptive Use
• Example: RESERVOIR
• Permanent
The User
Transfer To
Non-Consumptive Use
• Example: GOLF COURSE
• Temporary
Of Time
Grant Of Partial
Control To User For A Period
Both Consumptive and Non-Consumptive Use
• Example: HOTEL
• Temporary Grant Of Room For A Period Of Time
• Guest could destroy room or entire wing of hotel, which is Permanent Capacity Consumption
© 2005 Employers Reinsurance Corporation
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1. “Rental” Or Non-
Consumptive
 Returns Meet Or Exceed
Expectation
 Capacity Is Occupied,
Then Returned
Undamaged
 A.k.a. Room Occupancy
2. Consumptive
 Results Deteriorate
 Reserve Strengthening Is
Required
 A.k.a. Destroy Your
Room, Your Floor, Or
Even The Entire Hotel
Charge portfolio segments for both uses of Capital
© 2005 Employers Reinsurance Corporation
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Two Kinds Of Charges:
1.
Rental = Access fee for LOC
 Function of Capacity Usage (i.e., Rating
Agency Required Capital)
 Opportunity Cost of Occupying Capacity
2.
Consumption = Drawdown fee for LOC
 Function of Downside Potential (i.e., segment economic shortfalls)
 Opportunity Cost of Destroying Future Capacity
Charge portfolio segments for Both Uses of Capital
© 2005 Employers Reinsurance Corporation
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EVA = Return – Cost of Capital Usage
Factors in:
> Capacity Usage (finite supply, driven by external
S&P requirements)
> Company Risk Appetite
> Product Volatility
> Correlation of Product with Portfolio
Powerful Decision Metric For Your Consideration
© 2005 Employers Reinsurance Corporation
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1.
Downside = Max(Simulated Loss > Expected
Loss, 0)
2.
Capital rental charge (access fee)
( Ex: 10% of required capital balance )
3.
Charge for drawdown on required capital
(damage your room)
( Ex: 50% of underwriting result)
4.
Charge for drawdown beyond required capital
(damage hotel)
( Ex: 100% of u/w result beyond capital allocation)
© 2005 Employers Reinsurance Corporation
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Capital Usage Charge Calculation Example
Charges:
(A) Rental = 10%
(B) Within Capital = 50%
(C) Beyond Capital = 100%
Loss – Exp Loss
Trial 1: +$2M
Trial 2: -$3M
Required Capital = $5M
Capital Usage Cost
$5M*10% =
$500K
$500K
+ $3M*50% = $2,000K
Trial 3: -$8M $500K + $5M*50% +
$3M*100% = $6,000K
Steepness of penalty depends on relative difference between (B)
Within Capital and (C) Beyond Capital charges
© 2005 Employers Reinsurance Corporation
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Sticking to the facts:
> Earn premium, set up reserve = EP*Plan LR.
> Remainder after expenses (if any) goes to underwriting profit that year .
For a LOB with any tail, reserve deterioration beyond Plan LR occurs in future years future capital .
, and therefore must be funded from
LOB profit shows up not in in required TM .
reducing the capital usage cost but increasing the EVA, or in comparisons of actual TM versus
Another advantage: avoids recursion in determining required
TM
© 2005 Employers Reinsurance Corporation
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Financial distress costs
> Impairment
> Downgrade
> Loss of market viability
> Loss of franchise value (present value of grwoth options or PVGO)
These increase with magnitude of capital depletion
Kreps makes a similar argument in his “Riskiness
Leverage Models” paper
© 2005 Employers Reinsurance Corporation
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© 2005 Employers Reinsurance Corporation
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Example 1
Property Catastrophe Contract
(1) Premium
(2) Limit
Capacity Occupation Cost
(3) Required Capital Factor
(4) Required Capital
(5) Opportunity Cost for Capacity
(6) Capacity Occupation Cost
Capital Call Cost
(7) Probability
(8) Loss
(9) Capital Call Amount
(10) Capital Call Cost Function
(11) Capital Call Charge
(12) Expected Capital Call Cost
EVA
(13) Expected NPV
(14) Expected Capital Usage Cost
(15) EVA
$ 500,000
$ 10,000,000
50.0%
$ 250,000
10.0%
$ 25,000
2.0%
$ 10,000,000
$ 9,500,000
50.0%
$ 4,750,000
$ 95,000
$ 300,000
$ 120,000
$ 180,000
Comments
= 5% Rate on Line
Rating Agency
= (3) * (1) r
Opp
= (4) * (5)
Full limit loss
= (8) - (1)
= 5 * r
Opp
= (10) * (9)
= (11) * (7)
= (1) - (7) * (8)
= (6) + (12)
= (14) - (15)
© 2005 Employers Reinsurance Corporation
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Example 2
Longer Tail Excess of Loss Contract
(1) Premium
(2) Limit
Capacity Occupation Cost
(3) Required Capital Factor - Premium
(3a) Required Capital Factor - Reserves
(3b) Reserve Amount
(3c) Reserve Duration
(4) Required Capital
(5) Opportunity Cost for Capacity
(6) Capacity Occupation Cost
Capital Call Cost
(7) Probability
(8) Loss (NPV @ 5%)
(9) Capital Call Amount
(10) Capital Call Cost Function
(11) Capital Call Charge
(12) Expected Capital Call Cost
EVA
(13) Expected NPV
(14) Expected Capital Usage Cost
(15) EVA
$ 500,000
$ 10,000,000
50.0%
35.0%
$ 156,705
5.00
$ 524,234
10.0%
$ 52,423
2.0%
$ 7,835,262
$ 7,335,262
50.0%
$ 3,667,631
$ 73,353
$ 343,295
$ 125,776
$ 217,519
Comments
= 5% Rate on Line
Rating Agency
Rating Agency
Years
= (3) * (1) + (3a) * (3b) * (3c) r
Opp
= (4) * (5)
Full limit loss, discounted
= (8) - (1)
= 5 * r
Opp
= (10) * (9)
= (11) * (7)
= (1) - (7) * (8)
= (6) + (12)
= (14) - (15)
Argument that Opp Cost should get larger over time ~ comparable to the liquidity premium argument for a positively sloping yield curve
© 2005 Employers Reinsurance Corporation
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© 2005 Employers Reinsurance Corporation
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1) Loss Generator
LOB 1
Log N Mu
Log N Sigma (~CV)
13.771
30.0%
Expected Loss 1,000,000
Profit Margin
Variable Expense Ratio
5.0%
0.0%
Plan Premium 1,052,632
Expected Loss Ratio 95.0%
Return $
Plan Loss Ratio
52,632
95.0%
Plan Loss $ 1,000,000
LOB 2
13.691
50.0%
1,000,000
5.0%
0.0%
1,052,632
95.0%
52,632
95.0%
1,000,000
LOB 3
13.571
70.0%
1,000,000
5.0%
0.0%
1,052,632
95.0%
52,632
95.0%
1,000,000
TOTAL
3,000,000
3,157,895
157,895
3,000,000
• Simplistic simulation model to demonstrate concepts
• “Risk” represented by differences in LogN sigma
(CV)
• Can also reflect “stretch” = [Plan LR – True Exp LR]
© 2005 Employers Reinsurance Corporation
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• One way to express “risk appetite” or “risk preference” or “emphasis”
• Determines which LOB pays how much for downside / volatility
• Must be calibrated to portfolio total
• Differences between (B) and (C) reflect “kurtosis penalty” – punishing tails
Required Capital Charge on Premium
Capital Usage Charge Adj Factor Due to Reserves
(A) Rental Fee
(B) Consumption Charge Within Required Capital
(C) Consumption Charge Beyond Required Capital
Required Premium Capital
3) Capital Usage Calculation
LOB 1
41.2%
100.0%
5.0%
10.0%
30.0%
433,333
LOB 2
41.2%
100.0%
2.00
6.00
433,333
LOB 3
41.2%
100.0%
433,333
© 2005 Employers Reinsurance Corporation
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RORAC = Return on Risk
Adjusted Capital
> Most capital allocation approaches
> Risk adjusted capital amount
> Constant cost of capital rate
RAROC = Risk Adjusted Return on Capital
> Risk adjust the return
> Only to the extent that capital amount does not reflect risk
100%
RAROC
An
Ap yw
Th pro he is L
Ca ac ine pita h C l C an lon g ost
Lie
Risk-Adjust Capital
© 2005 Employers Reinsurance Corporation
100%
RORAC
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4) Portfolio Evaluation Metrics - RAROC
LOB 1
Premium 1,052,632
Required Capital
Return
433,333
52,632
Expected Capital Usage $ Cost
EVA $
Usage Cost as % of Capital
28,447
24,184
Rental Fee
Consumption Charge
P [Exceeding Required Capital]
6.6%
5.0%
1.6%
11.0%
LOB 2
1,052,632
433,333
52,632
38,318
14,313
8.8%
5.0%
3.8%
16.0%
4) Portfolio Evaluation Metrics - RORAC
LOB 1
Premium 1,052,632
Required Capital 160,251
Return 52,632
Expected Capital Usage $ Cost
EVA $
Usage Cost as % of Capital
Rental Fee
Consumption Charge
P [Exceeding Required Capital]
14,793
37,838
9.2%
5.0%
4.2%
30.0%
LOB 2
1,052,632
393,536
52,632
36,328
16,303
9.2%
5.0%
4.2%
17.0%
LOB 3
1,052,632
433,333
52,632
53,241
(609)
12.3%
5.0%
7.3%
17.0%
TOTAL
3,157,895
1,300,000
157,895
120,006
37,889
9.2%
5.0%
4.2%
9.0%
LOB 3
1,052,632
746,213
52,632
68,885
(16,253)
9.2%
5.0%
4.2%
15.0%
TOTAL
3,157,895
1,300,000
157,895
120,006
37,889
9.2%
5.0%
4.2%
9.0%
© 2005 Employers Reinsurance Corporation
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1) Bonehead RAROC: Capital charges (amounts) reflect exact opposite opinion of our volatility measure (sigma) – how does the RAROC correct for this?
2) VaR (99%) RORAC: Capital charge relativities based on standalone VaR (99%) for each LOB.
How much “risk” remains unreflected – that is, how much do the returns have to vary?
© 2005 Employers Reinsurance Corporation
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1.
Determine the profit margins that give zero
EVA for each LOB
>Try one LOB at a time using Goal Seek
>Then simultaneous solution using Solver
Assess interdependence effects
2.
Same exercise but set stretch at: +5 pts LOB
1; 0 for LOB 2; -5 pts for LOB 3
Assess sensitivity to stretch
© 2005 Employers Reinsurance Corporation
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© 2005 Employers Reinsurance Corporation
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1
An Internal Risk Model Captures
Product-Inherent Risk Features
2
Product Performance Simulation
Produces Outcome Distributions
IRM Outcome Distributions
Parameters &
Distributions
Stochastic
Modeling
• Retro Program
• Cat Scenarios
• Dependency Structure
Trial # Segment 1 Segment 2 Segment 3
1 (368,800) (140,236) 496,560
2
3
…
(189,798)
(373,932)
267,062
(285,380)
622,633
(184,926)
9,999
10,000
88,373
(280,758)
938,368
222,965
(837,102)
813,636
TOTAL
(12,475)
699,899
(844,235)
199,639
765,843
3
Capital Usage Costs Are
Allocated To Segments
Rating Agency Required
Capital Constraint
4 Multiple Possible Uses
Determine Portfolio
Composition That…
Assess Risk-Adjusted
Target Price Levels
Volatility
And
Capacity
Risk-Based Cost
Of Capital Usage
Correlation s
Capital Usage Cost is an Expense Load that is a
Function of Volatility & Capacity Occupancy
Maximizes
EVA
Minimizes
Volatility
Optimization Metric Reflects Company’s Risk Appetite
© 2005 Employers Reinsurance Corporation
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Calibrate Total Capital Usage Cost to X% of
Required Capital
Can control emphasis of the RAROC formula:
 Capacity-focused: Majority of Usage Cost comes from Capacity Charges
 Volatility-focused: Majority of Usage Cost comes from Volatility Charges
 Balanced: 50% from each
© 2005 Employers Reinsurance Corporation
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Input
Portfolio Mix :
Premium, Loss Ratio,
Commission,
Overhead
Required Capital
Factors :
Premium And
Reserves
Capital Usage
Cost Factors :
Rental And
Consumption
Alternative
Mix
Evaluation
Perfect For “What-If” Analyses
© 2005 Employers Reinsurance Corporation
Output
Portfolio
EVA
Portfolio Capital
Usage Cost
Portfolio
DVS
Marginal Comparisons
With Other Mixes:
Required Premium Capital By Segment
Capital Usage Cost % By Segment
35

Optimizer
Inputs
Optimizer
Output
Segment
Premium
Constraints
Optimizer Evaluates
Thousands Of
Alternative Mixes
Input Output
Optimizer
Target:
E.g., Maximize
EVA
Portfolio Mix :
Premium, Loss Ratio,
Commission, Overhead
Required Capital
Factors :
Premium and Reserves
Mix Evaluation
EVA
Risk-Adjusted
Required TM by
Segment
Capital Usage
Cost Factors :
Rental and
Consumption
Marginal
Comparisons with
Other Mixes
Max
Required
Capital
Constraint
Perfect For Strategic Directional Analysis
© 2005 Employers Reinsurance Corporation
“Optimal”
Portfolio Mix
Given
Constraints
-
Evaluation
Metrics For
Optimal Mix:
-
EVA
DVS
Capital Usage Cost
Marginal
Comparison
With Starting
Mix
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3.
Market dictates that profit margin = 10% for all LOB.
>Determine the optimal portfolio mix that uses all the required capital using
Capacity-focused emphasis
4.
Same exercise but now use Volatilityfocused emphasis
5.
Find the mix that maximizes EVA $
6.
Find the mix that minimizes volatility while using all the required capital
© 2005 Employers Reinsurance Corporation
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© 2005 Employers Reinsurance Corporation
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Risk Adjusted Cost of Capital
Issue How It Will Be Addressed
Rating Agency Required
Capital is a Binding Constraint
But Rating Agency Capital
Charges do not reflect Our
Risks
Total Capital is really a
Shared Asset simultaneously exposed by all P&L’s
Use Rating Agency Required
Capital formula everywhere
Vary the Target Rates of
Return instead of varying the capital amounts (RAROC)
Capital Usage Cost formula works as if Finance grants the
P&L’s Letters of Credit:
 Assess a capacity charge
(like an access fee), and
 a volatility charge (like a draw down of the LOC)
© 2005 Employers Reinsurance Corporation
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1.
Complete framework that can handle both current approaches and future expansions
2.
Accessible underlying philosophy
3.
Reflects fundamental indivisibility of company capital
5.
6.
7.
Ties to Finance Dept by using external required capital formulas
Adjusts for degree of risk reflected in external required capital formulas
Risk preferences are explicit
4.
More realistic financial analogue than imputed equity flows = Letter of
Credit
8.
Reflects capacity occupation, volatility, risk preferences and correlations
© 2005 Employers Reinsurance Corporation
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This material has been submitted to both
ASTIN Bulletin
Copies of working paper, presentations, and demo model available from
Don.Mango@GE.com